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A006157 a(n+1) = (n-1)*a(n) + n*n!.
(Formerly M3950)
4
1, 5, 28, 180, 1320, 10920, 100800, 1028160, 11491200, 139708800, 1836172800, 25945920000, 392302310400, 6320426112000, 108101081088000, 1956280854528000, 37347179950080000, 750144785854464000, 15813863053148160000, 349121438173347840000 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

COMMENTS

Number of ascending runs of length at least two in all permutations of [n]. Example: a(3)=5 because we have (123), (13)2, 3(12), 2(13), (23)1 and 321, where the ascending runs of length at least 2 are shown between parentheses. - Emeric Deutsch and Ira M. Gessel, Sep 07 2004

REFERENCES

J. Francon, Histoires de fichiers, RAIRO Informatique Théorique et Applications, 12 (1978), 49-62.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Table of n, a(n) for n=2..21.

FORMULA

a(n) = (2n-1)/6 * n!.

E.g.f.: x^2*(3-x)/(6*(1-x)^2). - Emeric Deutsch and Ira M. Gessel, Sep 07 2004

MATHEMATICA

Table[(2n-1)/6*n!, {n, 2, 30}] (* Harvey P. Dale, Jan 06 2014 *)

CROSSREFS

Cf. A014484.

Sequence in context: A082031 A020081 A095676 * A179326 A156629 A123776

Adjacent sequences:  A006154 A006155 A006156 * A006158 A006159 A006160

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Simon Plouffe

EXTENSIONS

More terms from Harvey P. Dale, Jan 06 2014

STATUS

approved

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Last modified August 27 17:19 EDT 2015. Contains 261095 sequences.